You can but you (MAY*) have to use a zip archive utility to do it. You can't get at the graphic from Writer's user interface.

If you open the document from a zip archive tool (or 7zip, whatever), you'll find a folder named "Pictures" that contains all the embedded graphics. They all have weird names--long strings of digits--so you'll have to display each one to find which is the watermark. Once you know which one you want, you can extract it to a new file.

Edit: PS:

* If the watermark was added by Insert > Picture ... or copy/paste, you can just right-click on it and use Save Graphics ... and avoid the zip route altogether.